Purity of the single frequency mode of a hybrid semiconductor-fiber laser

The penalty of extending the cavity length of a laser diode when seeking a linewidth reduction is normally revealed by poor side mode suppression, which prevents the laser from operating purely in a single mode of the external cavity. A hybrid laser, based on a C-band semiconductor optical amplifier combined with a long erbium doped fiber external cavity, is carefully engineered to operate with high spectral purity and outstanding stability. For the first time, a side-mode suppression ratio of ≥42 dB, measured at a resolution of 1.16 pm (149 MHz) at all intra-cavity powers above the lasing threshold, is reported. The output power at the peak lasing wavelength is 13.3 dBm. Also, the ability to lock such a hybrid laser to a particular external-cavity mode is realized for the first time. Excluding the effect of mechanical and thermal drifts on the cavity length, the longterm frequency stability is demonstrated to be within ± 11 Hz while the long-term linewidth is 2.26 kHz, measured using the self-beating technique under free running conditions. ©2015 Optical Society of America OCIS codes: (140.3570) Lasers, single-mode; (140.3425) Laser stabilization; (140.2020) Diode lasers; (060.3510) Lasers, fiber; (060.2410) Fibers, erbium; (060.3735) Fiber Bragg gratings. References and links 1. J. Cliche, Y. Painchaud, C. Latrasse, M. Picard, I. Alexandre, and M. Têtu, “Ultra-narrow Bragg grating for active semiconductor laser linewidth reduction through electrical feedback,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest (Optical Society of America, 2007), paper BTuE2. 2. F. Aflatouni, B. Abiri, A. Rekhi, H. Abediasl, H. Hashemi, and A. Hajimiri, “Electronic laser phase noise reduction,” in Radio Frequency Integrated Circuits Symposium (IEEE, 2013), pp. 265–268. 3. L. Rodríguez-Cobo, M. A. Quintela, S. Rota-Rodrigo, M. López-Amo, and J. M. López-Higuera, “Singlelongitudinal mode laser structure based on a very narrow filtering technique,” Opt. Express 21(8), 10289–10294 (2013). 4. R. E. Bartolo, C. K. Kirkendall, V. Kupershmidt, and S. Siala, “Achieving narrow linewidth low-phase noise external cavity semiconductor lasers through the reduction of 1/f noise,” Proc. SPIE 6133, 61330I (2006). 5. Y. Painchaud, M. Aubé, G. Brochu, and M. Picard, “Ultra-narrowband notch filtering with highly resonant fiber Bragg gratings,” in Advanced Photonics & Renewable Energy, OSA Technical Digest (Optical Society of America, 2010), paper BTuC3. 6. K. Zhang and J. U. Kang, “C-band wavelength-swept single-longitudinalmode erbium-doped fiber ring laser,” Opt. Express 16(18), 14173–14179 (2008). 7. J. Tang and J. Sun, “Stable and widely tunable wavelength-spacing single longitudinal mode dual-wavelength erbium-doped fiber laser,” Opt. Fiber Technol. 16(5), 299–303 (2010). 8. X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filterstabilized external-cavity diode lasers,” Opt. Commun. 266(2), 609–613 (2006). 9. W. H. Loh, R. I. Laming, M. N. Zervas, M. C. Farries, and U. Koren, “Single frequency erbium fiber external cavity semiconductor laser,” Appl. Phys. Lett. 66(25), 3422–3424 (1995). 10. H. Rideout, R. Liu, J. Seregelyi, S. Paquet, and R. Kashyap, “Microwave signal generation using an erbium-doped external cavity laser,” Proc. SPIE 7099, Photonics North, 70990O (2008). #237905 $15.00 USD Received 13 Apr 2015; accepted 1 Jun 2015; published 9 Jun 2015 © 2015 OSA 15 Jun 2015 | Vol. 23, No. 12 | DOI:10.1364/OE.23.


Introduction
Cost-effective, simple structure and compact laser sources with high spectral quality are sought by many segments of industry.For instance in the telecommunication industry, the growing problem of transmission capacity congestion has led to the deployment of the dense wavelength-division-multiplexed (WDM) systems utilizing the broad spectral window of optical fiber links.However owing to the ever increasing demand for higher transmission capacities, portable laser sources with ultra-narrow linewidth and high spectral stability form a significant milestone for a solution, especially in coherent detection.In recent years, linewidth reduction methods of semiconductor lasers have improved significantly.The linewidth of a commercial distributed feedback (DFB) laser diode, for example, was reduced from 200 kHz to 2 kHz by optimizing an electrical feed-back loop [1].Another method was developed by subtracting the measured phase noise from the phase of the laser in an electro-optical feedforward loop, by which a 6-MHz linewidth of a DFB laser diode was reduced to 250 kHz [2].
Alternatively, passive wavelength selective elements such as fiber Bragg gratings (FBGs), employed as the basis of fiber external cavity lasers (FECLs), offer inherently narrower linewidth of the order of a few kilohertz [3] and the capability of mass production with lower noise [4] and better wavelength control [5].The self-induced FBG filter in erbium doped fiber (EDF), based on the principle of spatial-hole burning, has been advantageously utilized for single-longitudinal mode [6] and dual-wavelength [7] erbium-doped fiber lasers.Thus, hybrid FECLs provide a simple, potentially low cost and small footprint solution with high beam quality and low noise floor.However when the cavity is extended, the external-cavity mode spacing decreases as well, which is normally finer than the bandwidth of the FBG and leads to multi-mode operation.In order to produce a single-frequency device, a band-stop filter with a finer resolution than that of the FBG is required [8].Placing a piece of EDF (saturable absorber) in the external cavity was demonstrated as an impressive solution [9].Indeed, the presence of the long FBG, self-induced through saturable absorption, enhances not only the selectivity of a single operating mode but also the wavelength stability.By virtue of the longlived upper state of erbium ions (Er 3+ ) whose radiative lifetime is ~10 ms, a maximum cut-off frequency is set [10] so that the hybrid laser is unable to react to faster instabilities, whether originating from the SOA dynamics or due to environmental effects.Eventually, the operating wavelength may be locked using a modest low-frequency feedback control system [11].Over the past two decades, research effort has been focused on designing, stabilizing and enhancing the spectral purity of FECLs [9,[12][13][14][15].In fact, single-frequency operation was verified but the output power was low compared to results previously reported on FECLs without intracavity doped fiber [12,13].Later, the output power at the lasing wavelength peak was enhanced to ~14 dBm, but this time with a poor SMSR of only 10 dB [14].This problem was afterwards addressed and the SMSR was enhanced to 16 dB [15].However, the output power was not specified and the single-frequency regime was also found to deteriorate depending on the semiconductor optical amplifier (SOA) drive current or, equivalently, on the intra-cavity power.The best long-term stability of single-frequency operation with a high SMSR of an erbium doped FECL was measured to be primarily within ± 1.5 pm ( ± 193 MHz) [16].
In this paper, we report a hybrid semiconductor laser, in which the external cavity is made entirely of EDF.An unprecedented high spectral quality of the laser is demonstrated when operating under free running conditions.Its long-term linewidth, spectral stability, SMSR and power at the wavelength peak are reported.The optical measurements, taken with a high spectral resolution optical spectrum analyzer (OSA), are confirmed by RF measurement techniques using an electrical spectrum analyzer (ESA).Special attention is paid to specify the operating parameters for any potential application.We believe these results confirm the possibility of a low cost solution for compact lasers with ultra-high performance.

Device set-up
Our device is constructed from a 34-cm-long fiber cavity, coupled to a single angled-facet SOA (SAF 1126 from Covega) via a fiber lens as schematically illustrated in Fig. 1(a).The fiber cavity is made of a piece of PM-EDF, PANDA fiber from CorActive with a birefringence of 1.14 × 10 −4 , whose one end is sculpted into a biconic lens with an FBG directly written on the other end.The absorption of this PM fiber is measured at 1528 nm to be ~30 dB/m.The SOA is designed for C-band operation with a maximum optical gain of ~19 dB at a current of 350 mA.The reflectivity of the rear-facet of this SOA is enhanced to R = 90% while the front facet is anti-reflection (AR) coated.The waveguide is tilted relative to the AR facet to suppress any residual reflection and hence, its actual reflectivity is reduced to ~10 −5 [17].Most of the inherent feedback, attributed to any resonant cavity formed between the chip facets and the front end of the fiber lens, is therefore weakened and axial mode instabilities are removed [18].The fiber lens has an asymmetric focus, designed to couple the diverging light beam from the SOA into the fiber core with high efficiency.In the coherence collapse regime, the laser operates within the entire optical bandwidth of the FBG.A centimeter away from the FBG and outside the cavity, the PM-EDF is spliced to a 52-cm-long piece of PM fiber, terminated by an FC-APC connector.The fiber cavity is inspected by a Luna (OBR 4600) optical backscatter reflectometer as shown in Fig. 1(b).The various sections of the cavity can be discerned easily from the spatially resolved back-scattered signal.The 1-cm-long FBG with a peak reflectivity of 5.2 dB (70%) at a Bragg wavelength ~1527.8nm is raised-cosine apodized to suppress secondary lobes.The SOA, positioned by a Nanomax six-axis translation stage assembly, is optically coupled to the fiber cavity by placing the waveguide port at the focal point of the fiber lens, where the polarization axes of both the laser diode and the slow axis of the PM fiber cavity are aligned.Thus, the higher the coupling efficiency, the lower the lasing threshold so that the EDF absorption can be sufficiently bleached [19].The temperature of the fiber cavity and the SOA are stabilized using a laser driver LDC-3900.

Single-frequency operation
The quantitative information of the transfer characteristics and spectral dependence of an FBG can be obtained from the coupled-mode equations, given as #237905 -$15.00USD where ( ) R z and ( ) S z , the amplitudes of the coupled forward-going (reference) and backward (signal) identical modes propagating in the + z and -z directions, respectively.ac κ is the "AC" coupling coefficient while σ is the general "DC" self-coupling coefficient.Solving Eq. ( 1), the FBG power reflectivity is given as The FBG length, L, may be divided into subsections, whose optical parameters are assumed to be constants.The FBG power reflectivity can be calculated using the transfermatrix method [20], where the output parameters of each subsection containing the reflectivity, transmission and phase are the input for the subsequent sections.Considering the periodically spatial variation of refractive index , the coupling coefficient of the dynamic grating is estimated as [20]. 2 .
Thus considering the whole length of the fiber cavity 34.26 cm L = , the power reflectivity of the dynamic grating reflectivity is simulated and shown in Fig. 2 (a,b).On the other hand, the coupling coefficient of the apodized external FBG has functional dependence on the spatial parameter z over 1.1 cm and is given as The power reflectivity of the external FBG is simulated and shown in Fig. 2(a).The SOA's broadband emission is from 1500 to 1600 nm.The lasing wavelength, which normally drifts towards 1515 nm where the intra-cavity loss is at a minimum, is selected by the external FBG to be around 1528 nm.The mode spacing, , is calculated to be Δλ = 2.32 pm (298 MHz) at the wavelength peak λ = 1527.78nm.Thus, increasing the bias current up to the lasing threshold, around 34 external-cavity modes are allowed to oscillate within the FWHM = 80 pm of the external FBG's bandwidth.Their standing waves share the same node, located at the SOA's reflecting rear-facet and hence, they may share the same spatial hole-burning pattern in the close vicinity.On the other hand, the optical length of the SOA cavity is 3.35 mm so that the displacement between the side-mode patterns and the central one is at a maximum of ~ ± 86 nm from the AR front-facet.Each pattern is associated with a nonuniform distribution of excess electrons and holes.In fact, multi-mode operation is encouraged by such a nonuniform distribution.However in semiconductor lasers, the spatial diffusion of the carriers tends to wipe out the differences in carrier concentrations [21,22].In our SOA, that diffusion tends to smooth out the gain profile to some extent, which suppresses mode competition unless it is optically synchronized by developing a single dynamic grating centered at the Bragg wavelength of the external FBG.In this case, a fewer number of selected modes are iteratively fed by additional reflection and increasing power leading towards single-frequency operation.This can be explained based on the simulation, shown in Fig. 2, as the following.The external FBG is apodized to exclude the optical feedback of the side lobes and hence, to increase the SMSR of the laser.The FBG is centered at ~1527.8 nm as the EDF exhibits maximum photon absorption [19].Consequently, the standing wave intensity bleaches the fiber cavity absorption with the refractive index modulation, translated to a strong dynamic grating via the Kramers-Kronig effect [23].This self-induced FBG functions as a band-stop filter [24] with an FWHM of 2.16 pm selecting a single mode only within a double mode-spacing.A high SMSR can be realized as the other allowed modes have near zero reflectivity as shown in Fig. 2 (b).Consequently, the reflectivity and the phase of the reflected light from the external FBG and the optical feedback of the dynamic grating plays a key role in controlling mode competition.Owing to the spatial distribution of the bleached erbium ions in the silica-based fiber core, the reflectivity spectrum deviates slightly from the theoretical overlap between the allowed side modes and zero-reflections.This gives rise to weak side modes that are expected to be observed in the optical spectrum as will be shown later in Fig. 4(a) and Fig. 5(a).

Subcavity modes
By precise positioning, the reflection on the front end of the fiber lens may be sufficient to form a subcavity [25,26].The front facet of the SOA has an anti-reflection coating, so that the subcavity is formed between the fiber lens and the rear reflecting facet of the SOA.However, the subcavity optical length is determined by the number of the multi passes, N, made by the wave that has coupled back to the SOA cavity's field with an efficient field overlap [25].The effective field reflectance of the subcavity with the appropriate phase factor is expressed as , where f R is the reflectance of the fiber lens, n L is the optical length of a single pass in the subcavity.Also, the hybrid laser can be modeled as three coupled Fabry-Perot cavities: i.e., the chip, air and the fiber.The effective field reflectance of the equivalent cavity is given as [27] ( ) ( ) where R A is the reflectance of the AR facet while the FBG reflectance ( ) λ ρ is obtained from Eq. ( 2).The roundtrip gain in the fiber cavity is ( ) the fiber cavity loss coefficient, which is negligible when the absorption is fully bleached.
( ) Satisfying the resonance conditions at the same wavelengths, the subcavity and fiber cavity modes can be coupled and their reflectances add when they are phase matched.As a result, gain mode competition in the SOA is disturbed by the optical feedback of the subcavity, which gives rise to side modes whose amplitudes are determined by their spectral positions within the reflection profile of the external FBG.

Single-frequency operation & the dynamic grating
The device is connected to an isolator of ~52 dB return loss as schematically shown in Fig. 3(a).A bias current of 300 mA is used to drive the laser for 30 minutes.The photodetector receives ~9-dBm optical power and the generated photo current is directed to an Agilent (E4446A) ESA, whose resolution bandwidth filter (RBW) is set to 3 MHz and the trace is averaged.
The optical spectrum, shown in Fig. 4(a), is monitored on an APEX OSA (AP2050A), which has a resolution of 0.16 pm.A single, symmetrical and very sharp peak with a high relative peak-power confirms single mode operation and exhibits only weak side modes.A Burleigh (WA-1000) laser wave meter, with a resolution of ± 0.7 pm, verifies the presence of a dominant mode operating at a wavelength of 1527.780nm, in agreement with the OSA data.In the electrical spectra, plotted in Fig. 4(b), the noise floor is identified when the laser current source is switched off.With the laser switched on, the spectra are taken every 1 second for a period of 30 minutes and plotted together.No mode beats are observed.The only increase above the noise floor is detected within 0-3 GHz range by a maximum of 4 dB.These RF spectra show that there is only a single mode oscillating in the cavity.The amplitude of any RF beat-signals is lower than −74 dBm, which indicates a high SMSR.This confirms the previous results, obtained by the optical measurements.Consequently, a single oscillating mode is inferred.The laser's long-term spectral stability is measured using the APEX and monitored over a period of 45 minutes while the data is collected every 3.2 seconds.Even though the device operates as a free-running laser, the operating wavelength shows high stability.For the first time to our knowledge, such a long-cavity hybrid laser is locked to a single cavity-mode within spectral fluctuations of ± 0.2 pm ( ± 26 MHz) as illustrated in Fig. 4(c).

Side mode suppression & maximum power
While a narrower linewidth is intended as the main advantage of a long FECL, the penalty is usually seen by a poor SMSR preventing the ECL from operating with a linewidth of a single external-cavity mode.The enhancement in SMSR of a long FECL is still challenging as the mode spacing decreases with the cavity length.The highest SMSR, reported for a long cavity FECL with 28-cm-long intra-cavity EDF, was 16 dB [15].In order to measure the SMSR of our device, the same experimental setup is used as that in Fig. 3(a) except for the first coupler, whose 99%-port is connected directly to the APEX OSA.The absolute power accuracy of the APEX is ± 0.3 dB.The chip-fiber coupling is set to have a lasing threshold at a drive current of 84 mA.The equally-spaced weak side-modes are detected in the optical spectrum and a SMSR of 42 dB is measured as shown in Fig. 5(a).However at a bias current of 250 mA, the output power at the lasing wavelength peak increases to 11.24 dBm with an SMSR of 44 dB.Recalling Fig. 2(b) and as the SMSR is defined as the ratio of the power in the dominant mode to that of the strongest side mode, 44-dB SMSR is therefore measured at a resolution of Δλ/2 = 1.16 pm.Adjusting the chip-fiber coupling and at the maximum bias current of 350 mA, a higher power is obtained (13.3 dBm), which is very close to the highest peak power (14 dBm) reported previously with a ytterbium doped FECL [14], operating at 976nm.The latter device was, however, pumped by a high-power pigtailed laser producing 300 mW at the current of 500 mA.This shows a clear advantage of our device compared to the ytterbium doped fiber system, in which partial cavity-occupation of the dynamic grating was compensated for by a high intra-cavity flux to reduce the linewidth, following the Schawlow-Townes relationship [28].However, the downside was an increase in its side mode structure along with noise floor at high power.The observed SMSR may be confirmed by electrical measurements verifying the mode spacing.The tunable single-mode laser of the APEX is used for heterodyne detection.The experimental setup is shown in Fig. 3(b).The operating conditions of the hybrid laser are the same as the previous measurement, shown in Fig. 4(a).The electrical heterodyne spectra are plotted in Fig. 5(b).Owing to the 3-MHz linewidth of the APEX laser, the RF beat notes with the first side modes can be barely observed confirming a high SMSR of our device.However, the mode spacing is measured from the beating with the subsequent side modes.In good agreement with the optical measurements, it is found to be ~2.32pm (298 MHz).Also, the real-time spectrum of self-mode beating, plotted in Fig. 5(b), does not exhibit any beat notes as a direct result of a high SMSR.

Linewidth measurement & spectral stability expected for a packaged device
The demonstrated device is currently not packaged and the fiber lens of our device is held currently in free space.The cavity length fluctuates, as does the lasing wavelength, in response to the transient thermal drifts, associated with the variations in the power coupled through the chip-fiber connection.This severely restricts the resolution of linewidth measurement whether it is based on the delayed self-heterodyne interferometer or heterodyned with an external oscillator.Fortunately utilizing the coupled cavity modes, the electrical selfbeat notes are insensitive to the above-mentioned instabilities.Single-frequency operation deteriorates when forming a subcavity by tuning the temperature of the SOA and using a stepper motor of the Nanomax stage to adjust the cavity length.Its optical length is set to exactly one-tenth of the main cavity's optical length as deduced from the spectral positions of the subcavity modes, observed in the optical spectrum shown in Fig. 6(a).The conditions for the formation of this coupled subcavity are sustained for ~18 seconds and are found to be easily altered to accommodate another subcavity, which in turn initiates different operating modes.Nevertheless, alternative self-recovery of each subcavity is observed.It appears likely that the interplay between the two subcavities is governed by associated heat generation in the fiber cavity and the gain relations among the modes oscillating in the SOA [29].
The number of multi passes, N, constituting the subcavity length between the two reflectors can be estimated using the coupled-cavity model.Simply, any subcavity mode must be coupled to an allowed mode of the hybrid laser cavity to lase.Therefore, phase matching between the two modes has to be met while the subcavity optical length is precisely one-tenth of that of the hybrid laser cavity.In other words, any two consecutive subcavity modes have to spectrally overlap with two suppressed modes and must be exactly separated by 10 mode spacings of the hybrid external cavity.Using the effective field reflectance equations (Eq.( 5) & Eq. ( 6), the above-mentioned condition is only satisfied when the optical feedback of the subcavity is simulated with N = 15, according to which the results are plotted in Fig. 6(b).
In the electrical spectrum, the power of the strongest beat note, displaced in frequency by 10 mode spacings as shown in Fig. 7(a), is mainly attributed to the convolution of the dominant mode with the two strongest side modes.The linewidth of this beat note is normally twice the actual linewidth in single-frequency operation [30].Therefore, the ESA is centered at the frequency of that beat note as illustrated in Fig. 7(b) while the RBW is set to 6.8 kHz.The instantaneous linewidth of our laser is measured to be 2.238 kHz at 3 dB.The subcavity can only be coupled to a stable state of the hybrid laser while its allowed modes are locked by the condition of phase matching the subcavity modes.Thus within the formation time of the subcavity, the background noise is filtered out by the dynamic gratings and the long-term linewidth of the subcavity can be precisely captured using the self-beating technique.In this case, albeit the three subcavity modes oscillating in the main cavity are subject to the slow response of the associating long-lived dynamic gratings, the long-term frequency drift originates from the frequency fluctuations characterizing the subcavity's linewidth, given by [31] 2 .Consequently, the long-term linewidth is 22 Hz wider than the instantaneous linewidth.Therefore eliminating low-frequency mechanical and thermal drifts by a hermetically sealed package, the long-lived dynamic grating is expected to lock the operating frequency of our device to within ± 11 Hz for long-term single mode operation.

Conclusion
A hybrid semiconductor laser has been demonstrated with a 34-cm-long fiber external cavity.The external cavity is made entirely with PM-EDF without any passive sections.This configuration has been shown to be a significant improvement over previous doped FECLs.Theoretical modeling for mode selection has been performed to verify the conditions for single-frequency operation, which has been confirmed by optical and electrical measurements at any bias current above the lasing threshold.The hybrid laser has been locked to a particular external cavity-mode whose wavelength varies within ± 0.2 pm under free running conditions.The long-term linewidth has been measured to be 2.26 kHz with a high power of up to 13.3 dBm at the peak lasing wavelength.An SMSR of 44 dB has been demonstrated at a measurement resolution of 1.16 pm showing the linewidth of a single external-cavity mode.When the device is packaged properly, a long-term frequency stability within ± 11 Hz has been inferred.
The linewidth can be further reduced by extending the fiber cavity and hence, this hybrid laser provides an elegant and attractive single-frequency device for WDM systems, coherent systems as well as for RF optical generation using beat frequency in hybrid fiber radio networks, and as a simple source for nonlinear optics using amplification.

Fig. 1 .
Fig. 1.(a) Schematic of the hybrid laser.(b) Optical backscatter reflectometer (OBR 4600) spectrum illustrating the exact length of each fiber section in the FECL device, where the scan range of the OBR is set to 41 nm (1525-1566 nm).

Fig. 2 .
Fig. 2. (a) Simulated reflectivity of the external 1-cm-long FBG compared to that of the 34-cm dynamic grating.The dynamic grating is zoomed in (b) and shown along with the spectral locations (vertical lines) of the allowed equally-spaced cavity modes, which all have near zero reflectivity except the one in the main lobe.
gain in the gap d separating the fiber lens and the AR facet of the SOA, where air a denotes the related loss coefficient.

Fig. 3 .
Fig. 3. Experimental setup to (a) observe single-frequency operation of the hybrid laser and (b) to verify the mode spacing using heterodyne detection.

Fig. 4 .
Fig. 4. (a) Optical spectrum showing a single and sharp spike indicating single-frequency operation.(b) Averaged electrical spectra of the hybrid laser, collected every 1 second over a period of 30 minutes, are overlaid (dark lines) and compared to the noise floor spectrum (orange line) (c) Long-term wavelength stability within ± 0.2 pm is measured over a period of ~45 minutes and shown in terms of the mode spacing, where the spectral drift is offset to the operating wavelength and is normalized to the mode spacing Δλ = 2.32 pm.

Fig. 5 .
Fig. 5. (a) Optical spectra of the hybrid device illustrating the equally-spaced side-modes and their SMSRs at different drive currents.(b) Electrical spectrum of heterodyne beat notes compared to the self-mode beat spectrum.

Fig. 6 .
Fig. 6.(a) Optical spectrum of the hybrid device illustrating the subcavity modes along with the dominant mode, observed in single-frequency operation.The operating modes are spaced equally by 10 mode spacings.(b) Effective field reflectance, simulated as a function of the operating wavelength, is illustrated for the subcavity (blue line) and the hybrid laser (gray line).The reflection peaks of both are overlapped when the subcavity is constituted by 15 passes, which is exactly one-tenth of the hybrid device cavity.The resultant optical feedback disturbs mode competition and hence, the side modes are observed in the optical measurement and spaced at 10 × the mode spacing of the hybrid external cavity.

Fig. 7 .
Fig. 7. (a) Electrical spectrum showing the equally-spaced microwave self-beat notes of the operating modes, demonstrated in the optical spectrum in Fig. 6(a).(b) Linewidth measurement of the hybrid device using self-beating technique.The frequency is offset at 2986.8 MHz.The instantaneous linewidth is 2.238 kHz, half the width of the beat note whose frequency drift, 226 kHz, is demonstrated using the maximum hold option offered by the ESA.The long-term linewidth is deduced to be 2.26 kHz.The difference between the instantaneous and long-term linewidth, 22 Hz, represents the long-term spectral stability of this device once it is packaged.

τ
are the round-trip time of the SOA and external cavities, respectively, andSOA v Δis the virtual linewidth of the SOA chip without antireflection coating.Thus, the longterm linewidth of our single frequency laser, , the round-trip time of the subcavity and the main cavity producing single-frequency operation.The long-term linewidth is therefore